The day began exactly as it did on that fateful date 10 years ago: under a crystal-clear sky that heightened the colours of the city and made the surrounding skyscrapers sparkle. But despite the auspiciousness of the morning, there was no doubting its sombreness.

Where the Twin Towers stood until 9.59am and 10.28am respectively on 11 September 2001, two giant water features now cascaded following their official opening. The sound of water falling 30ft to the reflective pools below echoed around the glass cladding of the replacement towers rising around Ground Zero, creating the illusion of hundreds of people chattering.

Not long after dawn the sound of real chattering began to suffuse the area as a crowd began to form at the World Trade Centre. Not any crowd. Every individual there represented a decade of loss and mourning. Each one brought with them the memory of a father, wife, son - some in physical form like the woman who carried aloft a series of photographs of a man cut into shapes that spelled: "I love daddy". Others wore T-shirts with printed photos of their loved ones, or held up placards showing a husband at his college graduation, a daughter smiling broadly, with the words: "Never forgotten".

How to measure the enormity of the events of that day a decade ago, and what they signify today? You can quote statistics, like the headline figure of 2,977 – the number of those who died in New York, Washington and Pennsylvania (not including the 19 hijackers). Or you can cite the figure that almost half of those who died had children under 18.

But statistics only go so far. Another way of gauging the numbing scale of the tragedy was that it took four and a half hours to read out in alphabetical order the names of the victims. Those with a surname starting with "A" alone took almost 10 minutes - all 108 of them.

When the hijackers boarded the four planes at Boston, Newark and Washington that morning they had been drilled to believe that they were attacking the enemy of a monolithic America. But as the "As" were read out it became clear that the victims of al-Qaida's hatred were anything but monolithic. It was like being taken on a journey around the world: Abad, Aceto, Acquaviva, Adanga, Afflito, Afuakwah, Agarwal, Agnello, Ahladiotis, Ahmed, Alegre-Cua, Alikakos, Amanullah, Ang, Arczynski, Avraham ...

Ten years later, and the bereavement still boomed out loud and clear. Many relatives struggled to keep their composure, voices cracking, as they read out the name of their own loved-one. Strangely, one of the calmest speakers was also one of the youngest: a 10-year-old boy took the stage and said, without a glitch: " I wish I'd known you better, but I was nine months old when you died. Everybody says you were a great guy. I love you Dad."

But what the name-reading couldn't do was convey the myriad stories that lay behind each one. Take Gordon Aamoth, the first of the 2,977 to be proclaimed. His friends called him "Gordy". He was a keen athlete and captain of his high-school football team, and on the day before he died, aged 32, he clinched the largest deal of his career as an investment banker. He came to the World Trade Centre that morning to announce his success.

Or the very last name, Igor Zukelman. He arrived in New York in 1992 from his native Ukraine and built a new life for himself in a financial company. He used to boast to friends that from his 97th floor office in the Twin Towers you could see the whole of New York City, and he became an US citizen just months before he died, aged 29. He left behind a son, then aged three.

Though the politicians turned out in force, they did so tentatively, timidly almost, as though they knew that this was not their moment. For the first time, Presidents Obama and Bush were united at Ground Zero – Bush having declined an earlier invitation to appear here after the killing of Osama Bin Laden.

Obama read from Psalm 46 - "God is our refuge and strength" - after a minute's silence was held at 8.46am to mark the instant the first plane went into the North Tower. The president was standing just in front of the spot where the tower used to stretch far up into the sky; you could look up directly above his head and imagine the fireball at the 94th floor.

In his oration, Bush turned to Abraham Lincoln for inspiration, reading a letter his predecessor sent to a mother of five sons who died in the Civil War. "I feel how weak and fruitless must be any words of mine which should attempt to beguile you from the grief of a loss so overwhelming," Lincoln wrote.

Both Bush and Obama spoke from behind bullet-proof glass screens. That was a sharp reminder that the wound to America's sense of security that was inflicted 10 years ago has yet to heal.

So too was the 60-foot slap of concrete and steel that stands at the foot of the rising 1 World Trade Centre, the signature skyscraper that dominates the reborn site. The fortress-like wall was designed as a precautionary measure that would project America's strength and confidence; somehow it merely suggests the opposite.Away from Ground Zero, smaller gatherings marked aspects of the 9/11 tragedy in their own personal ways. Further uptown, at a fire station on 48th Street, firefighters and bereaved families remembered the firefighters of Engine 54, Ladder 4. Every member who reported for duty that day died, 15 in all.

Among those at the service yesterday was retired fire chief Joe Nardone, commander on 9/11. He said it was a day for remembering "broken hearts and unspeakable horrors".

"We have vowed to never forget and we never will," he said. He spoke of those 28 children of the firehouse who had grown up without fathers since 9/11 and paid tribute to the "inspirational" firefighters, who had, "with dignity and ceremony, carried their brothers' remains off the ramp to the street" amid the rubble of the Twin Towers.

Maureen Sparta, the sister of Lenny Ragaglia, better known as "Rags", who died on duty, said: "Everyone has made a big deal about it's 10 years but the number doesn't make a difference. It hurts just as much. I never stop missing him.

"We never found him" said Sparta. "So Lenny is still there."

In a field near Shanksville, Pennsylvania, where Obama travelled from Ground Zero to lay a wreath, thousands of people marked a moment of silence at 10.03am, the moment United flight 93 flew into the ground after 40 passengers and crew lost their battle to seize control of the plane from the hijackers.

Sorrow filled the speeches in Shanksville but also celebration, at times marked with jingoism, for the "extraordinary heroism" of the 40 passengers and crew who prevented the hijackers going on to attack the Capitol in Washington. A local congressman, Bill Shuster, echoed George Bush's sentiment on Saturday that the dead had launched the first blow of the war on terror in attempting to take the plane back from the hijackers.

"This is the place where Americans said no," said Shuster. "They fought the first counter-offensive in the skies over America. And it ended right here in Shanskville."There were differing views expressed at Shanksville on what the day meant. Beth Schaefer, who travelled from Wisconsin, spoke with tears in her eyes.

"My sister lives nearby and we spent three weeks together here after 9/11. I felt I had to come back. I wanted to be part of this day for a kind of closure. Not that I'll ever forget but it's time to move on," she said.

Jason Cassidy, a metalworker, came from Baltimore because he felt it was important to honour the dead. But he was frustrated at the tone of some of the speeches, which he felt cast the resistance of the passengers and crew to the hijackers as a justification for a wider war."We don't forget that day because we're still living it. It's not just history, it's now. Out of that day, a lot of people have died. Thousands more Americans. Thousands in Iraq and Afghanistan," he said.

"There are not enough people asking the question whether our response to what happened here has made it more not less likely we'll be attacked again."

But his note of scepticism was largely lost on this of all days. Mourners were not prepared for it.

Back at Ground Zero, as the last names were read out relatives assembled around the reflective pools. Some stared silently into the water, others laid red roses. But the children had the best idea.

They took rubbings of their parents' names that are now etched in bronze all around the pools' edges. They scratched away furiously, capturing in coloured crayons an image of their loss as though their own lives depended on it.